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Math Help - Area

  1. #1
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    Area

    Let R be the region bounded by the graph of y=(1/x)(ln(x)), the x axis, and the line x=e. Find the area of the region.

    So i found that (1/x)(lnx) intersects the x axis at 1 so to solve for the area we would find the intergral of (1/x)(lnx) from 1-e. How would i find the antiderivative of (1/x)(lnx) and is my method right? This is a Calc AB problem
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  2. #2
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    Quote Originally Posted by calc_help123 View Post
    Let R be the region bounded by the graph of y=(1/x)(ln(x)), the x axis, and the line x=e. Find the area of the region.

    So i found that (1/x)(lnx) intersects the x axis at 1 so to solve for the area we would find the intergral of (1/x)(lnx) from 1-e. How would i find the antiderivative of (1/x)(lnx) and is my method right? This is a Calc AB problem
    Integrate the function from 1 to e.

    use the substitution \ln x = u

    \frac{1}{x}dx = du

    The integral comes out \frac{(\ln x)^2}{2}

    Finish it.

    See the attached graph
    Attached Thumbnails Attached Thumbnails Area-g9.jpg  
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  3. #3
    Member OnMyWayToBeAMathProffesor's Avatar
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    I misunderstood this problem. when they said x=e for some reason i thought they meant x=e^y so then i tried to solve for y. now it makes sense.

    so the final product would be \int_1^e \frac{1}{x}\ln(x) = .5

    correct?
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